If conventional attacks under the protection of a nuclear umbrella were feasible, then why didn't the USSR ever invade western Europe under the protection of their nuclear umbrella?
Its because in real life it doesn't work like that.
nuclear non-proliferation
That is entirely the fault of the USA. THEY are the ones who have forced smaller nations to develop nukes for self protection from their aggression and invasions. Maybe they should have thought of that before Bush ruined all the progress Clinton made with NK.
development of nukes is extremely destabilizing
Actually nukes are a stabilising influence because they allow paranoid nations to feel secure. In fact without nukes we would have had several more world wars by now. No nuclear power has ever gone to war with another nuclear power. Therefore if every nation had nukes, there would be no more inter nation war.
Actually the only thing that makes the world more unstable are the ABM defenses America is creating, which forces nations to expand and upgrade their stockpile to maintain deterrent. In fact a nation may decide its in a position of use them or lose them and launch first against America before the ABMs can totally neutralise their deterrent.
There is a reason America is building ABMs. Its to make nuclear war winnable.
All they will do is make nuclear war inevitable.